Charge ordering in ${\text{La}}_{1.8-x}{\text{Eu}}_{0.2}{\text{Sr}}_x{\text{CuO}}_4$ studied by resonant soft x-ray diffraction

Resonant soft x-ray scattering with photon energies near the $\text{O}K$ and the $\text{Cu}{L}_3$ edges was used to study the charge ordering in the system ${\text{La}}_{1.8-x}{\text{Eu}}_{0.2}{\text{Sr}}_x{\text{CuO}}_4$ as a function of temperature for $x=0.125$ and 0.15. From the superstructure diffraction intensities, a charge ordering with a doping-dependent wave vector is derived which is in this system well below the transition temperature of the low-temperature tetragonal phase but well above the onset of spin ordering. This indicates that structural changes and magnetic interactions are not in general the driving force for the formation of stripelike phases in two-dimensional-doped cuprates. Analysis of the lineshape of the scattered intensity as a function of photon energy yields evidence for a high hole concentration in the stripes.

Figure 1

(Color online) (a) [(b)] The resonant scattering intensity in light gray (red) as a function of photon energy through the $\text{O}K$ $\left[\text{Cu}{L}_3\right]$ absorption edge for the stripe superstructure peak. Data were taken near the $\text{O}K$ $\left[\text{Cu}{L}_3\right]$ for $l=0.75$ (1.6). Also shown is the x-ray absorption spectrum in black and the calculated scattering intensity in dark gray (blue). (c) The real (solid line) and the imaginary (dotted line) parts of the atomic form factor $f$ at the $\text{O}K$ edge of LSCO for $x=0.07$ depicted in light gray (red) and $x=0.15$ depicted in dark gray (blue). (d). The real part in light gray (red) and the imaginary part in dark gray (blue) of the atomic form factor $f$ at the $\text{Cu}{L}_3$ edge of LSCO for $x=0.125$.

Figure 2

(Color online) (a) Temperature dependence of $h$ scans along $\left(h,0,l\right)$ showing superstructure reflections of LESCO ($x=0.125$ and 0.15) using $\text{O}K$ $\left(l=0.75\right)$ and $\text{Cu}{L}_3$ $\left(l=1.6\right)$ photon energies. Points depict RSXD data; the solid lines represent fits to the data. (b) Temperature dependence of the intensities of the superstructure reflections shown in (a) normalized to the intensity at $T=6\text{K}$. The dotted line is guide for the eyes $\left[\propto {\left(T_c-T\right)}^{1/2}\right]$. To highlight the existence of charge ordering above $T_{\text{SO}}$, the fit of data near $T_{\text{SO}}$ is marked by a black line in (a) and by arrows at $T_{\text{SO}}$ in (b). For $x=0.15T_{\text{SO}}$ was taken from neutron-scattering data (Ref. 14) and for $x=0.125T_{\text{SO}}$ was extrapolated from data in the literature (Refs. 6, 14).